Shakespeare partly owned the globe theatre. After he went back to Stratford, the theatre got less popular and maybe started "rotting".
Also, Shakespeare was an Actor. And one of his roles was the ghost in Hamlet. (Heaven will direct it (the ghost Hamlet --- > back to Stratfort))
And i know that Greene said something like Wisdom for a Penny ("Für einen Pfennig Weisheit" in German. dunno the correct translation).
This refers to Shakespeare as a person who thinks he is the best.
This also could mean that - if shakespeare really thinks so - he also thought that if he'd leave London, the true "Art" would rot. Cus only his plays were the real ones. And everyone else is stupiiid
And that would mean "something is rotten in the state...." and "heaven will direct it" either refers to his Art (Acting, Plays, Theatre) or to the person, london knew as shakespeare.